Odd-flavored QCD_3 and Random Matrix Theory

TL;DR

This paper explores the relationship between odd-flavored QCD in three dimensions and random matrix theory, establishing universality and connecting kernels to finite-volume partition functions.

Contribution

It introduces pseudo-orthogonal polynomials to relate QCD_3 with odd flavors to chiral random matrix ensembles, demonstrating universality in the microscopic limit.

Findings

Established parity invariance at classical level with zero masses.

Related kernels to chiral unitary ensemble with half-integer topological charge.

Proved universality and expressed kernels via finite-volume partition functions.

Abstract

We consider QCD_3 with an odd number of flavors in the mesoscopic scaling region where the field theory finite-volume partition function is equivalent to a random matrix theory partition function. We argue that the theory is parity invariant at the classical level if an odd number of masses are zero. By introducing so-called pseudo-orthogonal polynomials we are able to relate the kernel to the kernel of the chiral unitary ensemble in the sector of topological charge $\nu={1/2}$. We prove universality and are able to write the kernel in the microscopic limit in terms of field theory finite-volume partition functions.